Two Dimensional Mathematical Model of Unsteady Groundwater Flow through Non – homogeneous and Anisotropic Medium Using the Finite Difference Method, control Volume Approach

Abstract

Unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial
differential equation.' This-equation cannot be solved analytically. Hence, numerical methods. such as the finite
element and the finite difference methods might be employed.
In this study a mathematical model has been developed using the fully implicit finite difference method with
control volume approach. The discretized non - linear equations have been solved by the line by line sweeping
method with thomas algorithm in four directions. The model has shown a very good convergence, accuracy and
consistency' The accuracy of the model h-as been approved by a comparative study with the exact analytical
solutions of some well known problems.